Linear instability in planar viscoelastic Taylor–Couette flow with and without explicit polymer diffusion

IF 2.8 2区工程技术 Q2 MECHANICS

Journal of Non-Newtonian Fluid Mechanics Pub Date : 2025-07-21 DOI:10.1016/j.jnnfm.2025.105459

Miguel Beneitez , Soufiane Mrini , Rich R. Kerswell

引用次数: 0

Abstract

Elastic turbulence has been found in computations of planar viscoelastic Taylor–Couette flow using the Oldroyd-B model, apparently generated by a linear instability van Buel et al. (2018). We demonstrate that no such linear instability exists in the governing equations used unless some diffusion is added to the polymer conformation tensor equation, as might occur through a diffusive numerical scheme. With this addition, the polymer diffusive instability (PDI) Beneitez et al. (2023) exists and leads to chaotic flows resembling those found by van Buel et al. (2018). We show how finite volume or finite-difference discretisations of the governing equations can naturally introduce diffusive errors near boundaries which are sufficient to trigger PDI. This suggests that PDI could well be important in numerical solutions of wall-bounded viscoelastic flows modelled using Oldroyd-B and FENE-P even with no polymer stress diffusion explicitly included.

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平面粘弹性Taylor-Couette流动的线性不稳定性

在使用Oldroyd-B模型计算平面粘弹性Taylor-Couette流时发现了弹性湍流，这显然是由线性不稳定性van Buel等人（2018）产生的。我们证明，除非在聚合物构象张量方程中加入一些扩散，否则在所使用的控制方程中不存在这种线性不稳定性，这可能通过扩散数值格式发生。有了这个补充，聚合物扩散不稳定性（PDI） Beneitez et al.（2023）存在，并导致类似于van Buel et al.（2018）发现的混沌流动。我们展示了控制方程的有限体积或有限差分离散如何自然地在边界附近引入足以触发PDI的扩散误差。这表明，即使没有明确包括聚合物应力扩散，PDI在使用Oldroyd-B和FENE-P模拟的壁面粘弹性流动的数值解中也很重要。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Non-Newtonian Fluid Mechanics 物理-力学

CiteScore

5.00

自引率

19.40%

发文量

109

审稿时长

61 days

期刊介绍： The Journal of Non-Newtonian Fluid Mechanics publishes research on flowing soft matter systems. Submissions in all areas of flowing complex fluids are welcomed, including polymer melts and solutions, suspensions, colloids, surfactant solutions, biological fluids, gels, liquid crystals and granular materials. Flow problems relevant to microfluidics, lab-on-a-chip, nanofluidics, biological flows, geophysical flows, industrial processes and other applications are of interest. Subjects considered suitable for the journal include the following (not necessarily in order of importance): Theoretical, computational and experimental studies of naturally or technologically relevant flow problems where the non-Newtonian nature of the fluid is important in determining the character of the flow. We seek in particular studies that lend mechanistic insight into flow behavior in complex fluids or highlight flow phenomena unique to complex fluids. Examples include Instabilities, unsteady and turbulent or chaotic flow characteristics in non-Newtonian fluids, Multiphase flows involving complex fluids, Problems involving transport phenomena such as heat and mass transfer and mixing, to the extent that the non-Newtonian flow behavior is central to the transport phenomena, Novel flow situations that suggest the need for further theoretical study, Practical situations of flow that are in need of systematic theoretical and experimental research. Such issues and developments commonly arise, for example, in the polymer processing, petroleum, pharmaceutical, biomedical and consumer product industries.